OFFSET
1,6
COMMENTS
Equivalence is up to rearrangement of the order of elements in both series and parallel configurations.
A series configuration is a multiset of two or more parallel configurations and a parallel configuration is a multiset of two or more series configurations. The unit element is considered to be a parallel configuration.
FORMULA
Inverse Euler transform of A339153.
EXAMPLE
In the following examples, elements in series are juxtaposed and elements in parallel are separated by '|'. The unit element is denoted by 'o'.
a(1) = 1: (o).
a(4) = 1: (oo|oo).
a(5) = 1: (oo|ooo).
a(6) = 3: (oo|oooo), (ooo|ooo), (oo|oo|oo).
a(7) = 4: (oo|ooooo), (oo|o(oo|oo)), (ooo|oooo), (oo|oo|ooo).
PROG
(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(S=vector(n), P=vector(n)); P[1]=1; for(n=2, #S, my(t=EulerT(S[1..n])[n]); S[n]=EulerT(P[1..n])[n]; P[n]=t); P}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Nov 26 2020
STATUS
approved